Finite Group Databasebeta

← #10829265

Subgroups — #10829265

Order 768.

1336 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5611C211yesmaximal, characteristic
2C2×#5164C211yesmaximal, characteristic, complemented
3#82777C211yesmaximal, characteristic, complemented
4C2×#4793C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72054C211yesmaximal, characteristic, complemented
7#71692C211yesmaximal, characteristic, complemented
8#71679C211yesmaximal, characteristic, complemented
9#70268C211yesmaximal, characteristic, complemented
10#70175C211yesmaximal, characteristic, complemented
11#70154C211yesmaximal, characteristic, complemented
12#69927C211yesmaximal, characteristic, complemented
13#69917C211yesmaximal, characteristic, complemented
14#68874C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24132—31nomaximal, Sylow
17C22×#237—21no—
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C2×#935—21no—
25C2×D4×Dic3C2211yescharacteristic
26C2×C4×#67C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28#5611—24no—
29#5611—24no—
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×#888C2211yescharacteristic
32C2×#883—21no—
33C2×#878—21no—
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5164—24no—
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#818C2211yescharacteristic
48C2×#815C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4990—21no—
51#4987C2211yescharacteristic
52#4982—21no—
53#4977C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4961—21no—
56#4945—21no—
57#4793—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#547—31no—
65C2×#477—31no—
66C2×#440—31no—
67#2536—31no—
68#2033—31no—
69#2033—31no—
70#2000—31no—
71#2000D311yescharacteristic, complemented
72#1993—31no—
73#1955—31no—
74#1872—31no—
75#1872—31no—
76#1852—31no—
77#1852—31no—
78#1804—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C23×Dic3—21no—
86C23×Dic3—21no—
87C2×#237—28no—
88C2×#237—44no—
89C2×#237—44no—
90C22×C4×D3—21no—
91C22×C4×D3C2311yescharacteristic
92C22×Dic6—21no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—41no—
100C3×#121—22no—
101C3×#121—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217D411yescharacteristic
111#946—22no—
112#946—41no—
113Q8×Dic3—22no—
114Q8×Dic3—22no—
115#938—22no—
116#938—22no—
117#935—28no—
118D4×Dic3—22no—
119D4×Dic3D414yes—
120C4×#67—22no—
121C4×#67—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4D411yescharacteristic
137C2×C4×Dic3—21no—
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141D3×C4⋊C4—22no—
142D3×C4⋊C4—22no—
143#888—22no—
144#888D414yes—
145#883—28no—
146#878—28no—
147C3×#103—22no—
148C3×#102—41no—
149C3×C22⋊C8—22no—
150#835—22no—
151#835—22no—
152#832—22no—
153#832—41no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#830—41no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—41no—
161#818—22no—
162#818—22no—
163#815—22no—
164Dic3⋊C8—22no—
165#807—22no—
166C22×#41—61no—
167C22×SD16C2×D311yescharacteristic
168#547—64no—
169#547—64no—
170C2×C4⋊Q8—31no—
171C2×#123—61no—
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—61no—
175C2×C22⋊Q8C2×D311yescharacteristic
176C2×#121—31no—
177C2×#121C2×D311yescharacteristic
178C2×C4×Q8—31no—
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183#477—64no—
184#440—64no—
185C2×#107—31no—
186C2×#107—31no—
187C2×#107—31no—
188C2×C4⋊C8—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103C2×D311yescharacteristic
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×C22⋊C8C2×D311yescharacteristic
199C2×#97—31no—
200#398—61no—
201#394—61no—
202#388—61no—
203#388—61no—
204#382—31no—
205#380—31no—
206#380—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340C2×D311yescharacteristic
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C23×D3C2×D411yescharacteristic
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8#4112yescomplemented
222C2×C3×D4—24no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—22no—
243C2×#67—22no—
244C2×#67—24no—
245C2×#67—22no—
246C2×#67—42no—
247C2×#67—42no—
248C22×Dic3—24no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—24no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—42no—
255C22×Dic3—42no—
256C22×Dic3—42no—
257C22×Dic3—42no—
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261#237—432no—
262C2×C4×D3—24no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×Dic6—24no—
272C2×Dic6—42no—
273C2×Dic6—42no—
274C3×SD16—28no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8#4112yescomplemented
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—42no—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—42no—
288#217—24no—
289#217—24no—
290#217—22no—
291#217—42no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295C4⋊Dic3—24no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—42no—
303C4⋊Dic3C2×D412yes—
304C4⋊Dic3C2×D412yes—
305Dic3⋊C4—24no—
306Dic3⋊C4—22no—
307Dic3⋊C4—24no—
308Dic3⋊C4—42no—
309C4×Dic3—42no—
310C4×Dic3C2×D412yes—
311C4×Dic3C2×D412yes—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×#41—68no—
319C2×#41—124no—
320C2×#41—124no—
321C22×Q8—61no—
322C22×Q8C22×D311yescharacteristic
323C22×D4—21no—
324C22×D4—31no—
325C22×D4—61no—
326C22×D4C22×D311yescharacteristic
327C23×C4—31no—
328C23×C4—61no—
329C23×C4—61no—
330C23×C4—61no—
331C23×C4C22×D311yescharacteristic
332C2×SD16—22no—
333C2×SD16—22no—
334C2×SD16—22no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
339C4⋊Q8—34no—
340C4⋊Q8—62no—
341#123—68no—
342#123—68no—
343C22⋊Q8—22no—
344C22⋊Q8—41no—
345C22⋊Q8—68no—
346C22⋊Q8—62no—
347C22⋊Q8—121no—
348#121—22no—
349#121—22no—
350#121—62no—
351#121—62no—
352C4×Q8—62no—
353C4×Q8—62no—
354C4×D4—34no—
355C4×D4—62no—
356C4×D4—62no—
357C4×D4—62no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—31no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C42—31no—
385C2×C42—61no—
386#107—62no—
387#107—62no—
388#107—62no—
389C4⋊C8—62no—
390#103—22no—
391#103—62no—
392#103—62no—
393#102—41no—
394#102—62no—
395#102—121no—
396C22⋊C8—22no—
397C22⋊C8—62no—
398C22⋊C8—121no—
399C22⋊C8—121no—
400#97—62no—
401#95—61no—
402#95—61no—
403#95—61no—
404#95—61no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—22no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3AGL(1,ℤ/8)12yes—
419C23×C3C22×D411yescharacteristic
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3AGL(1,ℤ/8)12yes—
427C3×Q8—22no—
428C3×Q8—22no—
429C3×Q8—41no—
430C3×Q8—41no—
431C3×D4—22no—
432C3×D4—22no—
433C3×D4—48no—
434C3×D4—41no—
435C3×D4—41no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4H(5,𝔽2)11yescharacteristic
457C2×C3×C42−1+411yescharacteristic
458#67—28no—
459#67—48no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—48no—
470C2×Dic3—48no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3#12012yes—
482C2×Dic3#12012yes—
483C4×D3—48no—
484C4×D3—41no—
485C4×D3—41no—
486C4×D3—41no—
487C4×D3—41no—
488Dic6—48no—
489C3×C8—22no—
490C3×C8—41no—
491C3⋊C8—41no—
492C3⋊C8—41no—
493C24—21no—
494C24—31no—
495C24D3×D411yescharacteristic
496#41—1232no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—64no—
503C2×Q8—122no—
504C2×Q8—122no—
505C2×Q8#23712yescomplemented
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—62no—
515C2×D4—62no—
516C2×D4—62no—
517C2×D4—64no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4D3×D412yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—64no—
534C22×C4—64no—
535C22×C4—64no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—122no—
547C22×C4—122no—
548C22×C4—122no—
549C22×C4—122no—
550C22×C4—122no—
551C22×C4—122no—
552C22×C4D3×D411yescharacteristic
553C22×C4C23×D311yescharacteristic
554SD16—28no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8#23712yescomplemented
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—32no—
571C4⋊C4—32no—
572C4⋊C4—42no—
573C4⋊C4—62no—
574C4⋊C4—64no—
575C4⋊C4—64no—
576C4⋊C4—64no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—122no—
584C4⋊C4—122no—
585C4⋊C4D3×D412yes—
586C22⋊C4—24no—
587C22⋊C4—42no—
588C22⋊C4—62no—
589C22⋊C4—62no—
590C22⋊C4—64no—
591C22⋊C4—64no—
592C22⋊C4—122no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C42—32no—
596C42—32no—
597C42—122no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3C2×#12011yescharacteristic
613C22×C3#54611yescharacteristic
614C22×C3#54711yescharacteristic
615C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
616C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
617C22×C3#57811yescharacteristic
618C22×C3#57811yescharacteristic
619C2×D3—22no—
620C2×D3—22no—
621C2×D3—22no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C3×C4—41no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—81no—
630C3×C4#52511yescharacteristic
631C3×C4#53711yescharacteristic
632C3×C4#54811yescharacteristic
633C3×C4#55011yescharacteristic
634Dic3—22no—
635Dic3—22no—
636Dic3—41no—
637Dic3—42no—
638Dic3—42no—
639Dic3—81no—
640Dic3—81no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—32no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23#91412yes—
662C23C2×D3×D411yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667Q8—128no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4—68no—
674D4—128no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—128no—
703C2×C4—128no—
704C2×C4—128no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4C2×D3×D411yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×#23711yescharacteristic
722C2×C4C2×#23711yescharacteristic
723C2×C4#100411yescharacteristic
724C2×C4#101011yescharacteristic
725C8—22no—
726C8—41no—
727C8—121no—
728C8—121no—
729C2×C3—42no—
730C2×C3—82no—
731C2×C3#240711yescharacteristic
732C2×C3#300311yescharacteristic
733C2×C3#301111yescharacteristic
734C2×C3#330811yescharacteristic
735C2×C3#330811yescharacteristic
736C2×C3#334311yescharacteristic
737C2×C3#334311yescharacteristic
738D3—42no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—62no—
750C22—62no—
751C22—62no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22D3×#12011yescharacteristic
761C22#559111yescharacteristic
762C22#561111yescharacteristic
763C22C2×#91411yescharacteristic
764C22#577111yescharacteristic
765C22D3×AGL(1,ℤ/8)11yescharacteristic
766C22#577911yescharacteristic
767C4—42no—
768C4—41no—
769C4—42no—
770C4—62no—
771C4—62no—
772C4—81no—
773C4—122no—
774C4—122no—
775C4—121no—
776C4—241no—
777C4—241no—
778C4#558611yescharacteristic
779C4#559711yescharacteristic
780C4#559811yescharacteristic
781C4#571811yescharacteristic
782C3#2413211yescharacteristic, complemented, Sylow
783C2—42no—
784C2—82no—
785C2—122no—
786C2#7666811yescharacteristic
787C2#8005111yescharacteristic
788C2#8010911yescharacteristic
789C2#8014611yescharacteristic
790C2#8023011yescharacteristic
791C2#8065111yescharacteristic
792C2#8082911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×#5611C2
hypercenter#2000D3
hypocenterC3#24132
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#5164C2semidirect
3. #82777C2semidirect
4. C2×#4793C2semidirect
5. C3×#2000C2semidirect
6. #72054C2semidirect
7. #71692C2semidirect
8. #71679C2semidirect
9. #70268C2semidirect
10. #70175C2semidirect
11. #70154C2semidirect
12. #69927C2semidirect
13. #69917C2semidirect
14. #68874C2semidirect
15. #68806C2semidirect
71. #2000D3semidirect
221. C2×C3×Q8#41semidirect
280. C2×C3×C8#41semidirect
505. C2×Q8#237semidirect
566. C2×C8#237semidirect
782. C3#24132semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#56112
C2×#51642
#827772
C2×#47932
C3×#20002
#720542
#716922
#716792
#702682
#701752
#701542
#699272
#699172
#688742
#688062
#241323